`doorstopper` and triaxial rock stress measuring instruments

Transcription

February,
1969
Journal
of the
South
African
Institute
of Mining
305
and Metallurgy
THE 'DOORSTOPPER'
AND TRIAXIAL ROCK STRESS
MEASURING INSTRUMENTS DEVELOPED BY THE C.S.I.R.
By E. R. Leeman* (Visitor)
INTRODUCTION
The first references in the literature to the so-called C.S.I.R. 'doorstopper' strain
cell were made in 19641,2,3,4. These were the climax of nearly two years of experimental and developmental work with the instruments and the operating techniques
involved.
Since that time numerous field measurements have been made with 'doorstoppers'
and they have been developed to a stage where they are in commercial production
and are being supplied to users throughout the world. No detailed description of the
latest 'doorstopper' equipment has, however, appeared in print and this paper is
written to bring the literature up to date in this respect.
The triaxial strain cell was developed three years agoS, 6, 7and was first described
at the First Congress of the International Society for Rock Mechanics in Lisbon in
19668. Since that date laboratory tests and-particularly
important-field
tests7' 9
have demonstrated the validity and practicality of the instruments and techniques.
These instruments have also been developed to a stage where they have been released
for commercial production. In this form they are very different from those described
two years ago and a full description of them at this stage seems to be justified.
THE INFORMATION
SUPPLIED
BY 'DOORSTOPPER'
AND TRIAXIAL
STRAIN
CELLS
Both the 'doorstopper' and triaxial strain cells were designed specifically to determine the absolute stress in rock using an overcoring stress relieving technique. They
were not designed to measure changes in stress. They may, however, be used for the
latter purpose provided the glue which is used to stick the strain gauges to the rock
is known to possess sufficiently stable strain-time characteristics as not to affect the
accuracy of the results during the time the measurements are made.
The 'doorstopper' was designed primarily to measure the major principal stress
in situations where its direction and those of the two other principal stresses were
either known or could be assumed. For example, at great depth in undisturbed virgin
ground, it is reasonable to assume that the maximum principal stress is vertical and
that the other two lie in a horizontal plane. The borehole in which the 'doorstopper'
is installed would thus be drilled in the horizontal plane parallel to one of the minor
principal stresses, the direction of which would either have to be assumed or determined as described later. The stresses measured would be the vertical major principal
str~ss and the principal stress acting in a horizontal plane normal to the borehole
aXIS.
It is possible, as will be shown later, to obtained the complete state of stress using
'doorstoppers'. In this event, it is necessary to make measurements in three boreholes
drilled in any three known directions to each other and relative to a system of three
orthogonal axes.
The triaxial strain cell was designed to determine the complete state of stress in a
single borehole drilled in any direction in any stress field. At first glance it would
appear to supersede the 'doorstopper'. This is not necessarily true since there are
*Senior Chief Research Officer, National
Pretoria.
Mechanical Engineering Research Institute, C.S.I.R.,
~
--------
306
Journal of the South African Institute of Mining and Metallurgy
February, 1969
The 'doorstopper'and triaxialrock stressmeasuringinstrumentsdevelopedby the CS.I.R.-E. R. Leeman
situations, such as in coal and weak, soft rock where it might be impossible to obtain
the relatively long lengths of core necessary (20 in. long and 3-!-in. outside and 1tin.
inside diameter) to effect a satisfactory stress relief cycle when using the triaxial cell.
In using the 'doorstopper' a length of as little as 2 in. of 1i in. diameter core is
required for successful overcoring.
It has also been demonstrated in coal that unreliable stress results are given when
the stresses are obtained by multiplying the measured strain relief readings obtained
by doorstoppers by the elastic constants of the coal. If, however, an assimulator
(described later) is used to obtain the stresses very reliable stress results are obtained
with doors toppers. At present no assimulator has been evolved by which the stresses
can be obtained directly from triaxial strain cell strain readings. They still have to be
calculated using the elastic constants of the rock. Thus, in such materials as some coals
it would seem unwise to use the triaxial cell and preferable to use the doorstopper.
It is also possible that the triaxial strain cell could be used initially to obtain the
directions of the minor principal stresses after which doors toppers could be used in a
borehole drilled in a direction parallel to one of these stresses. The two instruments
may therefore be considered as complementary to one another.
It must furthermore be emphasized that both instruments depend upon linear
stress-strain behaviour of the rock during stress relieving and a knowledge of the
relationship between stress and strain on unloading. In this connection the discovery
that even fractured rock on unloading and reloading exhibits a reasonably linear
stress strain behaviour1°, the width of the unloading/reloading stress strain 'hysteresis'
being relatively small, gives hope that the stress measuring technique may even be
used in fractured rocks for stress determinations. This behaviour no doubt accounts
for the successful use of the assimulator in conjunction with doorstoppers for stress
determinations in some coals which could not be described as elastic materials in the
classical sense because of the presence of cracks, cleats, etc.
THE DOORSTOPPER
STRAIN
CELL
It should perhaps first be explained that the name 'doorstopper' was given to
these strain cells because of their resemblance in colour, shape and size in the early
days to the red rubber cylindrical blocks used as doorstops in most homes. The name
therefore possesses no scientific connotation whatever!
The principle underlying the 'doorstopper' method of determining the stress in rock
A borehole is drilled into the rock to the depth at which it is desired to measure
the stress. Strain gauges are glued on the flattened end of the borehole. The depth
of the borehole is then extended using the coring crown used to drill the borehole
to the original depth. This is in effect an overcoring or trepanning operation which
relieves the stresses present on the flattened end of the borehole and results in changes
of strain which are measured by means of the strain gauges. The strain readings are
multiplied by the elastic constants of the rock and the stresses which were present
on the end of the borehole before overcoring are obtained. If the relationship between
the stresses present on the flattened end of a borehole and those in the surrounding
rock is known, the stress in the surrounding rock (which it is desired to measure)
may be calculated.
The relationship between the stresses on the .flattened end of a borehole and those in the
surrounding rock
The stress at a point in the rock can be represented by the system of stresses crX,
cry, crz, 't'Xy, 't'yZ and 't'ZXillustrated in Fig. l(a). If a borehole be drilled as shown in
-
-
307
February, 1969 Journal of the South African Institute of Mining and Metallurgy
The 'doorstopper'and triaxialrock stressmeasuringinstrumentsdevelopedby the c.S.f.R.-E.
R. Leeman
Fig. l(b) in the Z direction of the co-ordinate system used to specify the directions
of the six stress components the stresses on the flattened end of the borehole will be
as shown in Fig. l(c). The stresses therefore which will be measured by strain gauges
glued on the flattened end of the borehole will be cr'x, cr'y and T'Xy. To obtain the
stresses crx, cry, etc. in the surrounding rock from the stresses measured on the end
of the borehole the relationship between them must be known.
rJy
fY
rJx
/Tx
crz
la)
CO-OROINATE
SYSTEM
OF
THE
STRESS
AT A POINT
IN THE
ROCK
MASS.
O"Y
~~/~
«= i~\~6( ~
j6~
~~/~
//
~Y:;
.
~h~
Ibl
STRESSES ON THE FLATTENEO END
OF A BOREHOLE
1
CI'X
~'ay
(d)
2
Cl
Iy
DISTRIBUTION OF STRESSES
ON THE END
OF THE BOREHOLE (ACC. VAN HEERDEN I
Fig. I-The
(c)
ENLARGEMENT OF THE FLATTENED
END OF A BORE HOLE
~A=O;
(e)
4>6=90.; 4>c=22S.
CONFIGURATION
GLUED
OF
STRAIN
ON THE END OF THE
stresses on the flattened end of a borehole
GAUGES
BOREHOLE
308
February, 1969
R. Leeman
No theoretical relationship has yet been derived. Laboratory measurements,
however, on loaded prisms and cylinders of steel, rock and araldite by Bonnecherell, 12
and Van Heerden13 using electrical resistance strain gauges and photoelasticity to
determine the stress distributions on the flat end of boreholes drilled into the specimens have thrown light on the subject. The object of their investigation was to
determine the effect of the stress components, crx, cry, crz, 'l"Xy,'l"YZand 'l"zx in the
rock upon the stress components cr'x, cr'y and cr'Xy acting upon the end of the borehole.
Xy as follows:
They wrote cr'x, cr'y and '1"'
cr'x = a crx + b cry + C crz
cr'y = a cry + b crx + C crz
'I"'Xy=
d 'l"Xy
and found the following values, for a, b, Cand d
a
b
C
d
Bonnechere
1.25
0
-0,75
(0.5
1.25
+
Van Heerden
1.25
-0.064
-0,75
\/)
(0.645
+ \/)
Other investigators have obtained other values, particularly for a but it is believed
that the above values are the most reliable available. The author is inclined to accept
the value of c obtained by Van Heerden since it is the result of several measurements.
It should be mentioned that
the author, resulted from using
necessary conditions of uniform
and caused the higher erroneous
the value of a = 1.53 obtained by, amongst others,
cubes instead of prisms in the laboratory tests. The
stress cannot be and were not achieved in the cubes
value of a to be obtained.
The value of d gives the effect of 'l"Xy upon strain readings from strain gauges
glued on the end of the borehole. Since 'I"Xy has the same effect as two normal stresses,
of equal magnitude and opposite sign, acting at right angles to each other and at
45 degrees to 'l"Xy,the value of d = 1. 25, the same as a would seem to follow.
The shear components "yZ and 'l"zx would appear to have no effect on the
stresses in the XY plane. Since they have the effect of only rotating this plane around
the X and Yaxes respectively strain gauges glued on it should not be influenced by
them.
The value of b = -0.064 is small and may be neglected. Hence we can write
cr'x
=1.25crx-0.75(0.645+\/)crz
(1)
cr'y
,,'XY
=1'25cry-0'75(0.645+\/)crz
=1.25'1"xy
The distribution
of
cr'y
cr'x
and
over the end surface of the borehole,
crx
cry
(2)
(3)
obtained
cr'y
is shown in Fig. l(d). As will be seen from this figure cr'x and
crx
cry
are constant over approximately
the middle third of the end of the borehole having
the values of a = 1. 25 and b = 0 (approx.). Strain measurements
should therefore
be made in this area.
photo elastically,
February, 1969
309
The 'doorstopper'
and triaxial
rock stress measuring
instruments
developed
by the CoSofoR.-E.
R. Leeman
The determination of the stresses from doorstopper strain readings.
(a) Measurements in one borehole only
Since only three strain measurements are made with a doorstopper during any
single overcoring operation it is not possible to obtain any more information than the
magnitudes and directions of the principal stresses acting on the end of the borehole
before overcoring (and thence of course the stresses in the surrounding rock as indicated previously).
Thus if measurements are to be made in only one borehole it should be drilled
parallel to one of the minor principal stresses. The end of the borehole then becomes
the principal plane in which the major and the other minor principal stress act.
If as shown in Fig. I(b) the borehole is drilled in a direction parallel to the crz
principal stress, the stresses cr'x, cr'yand ,,'XY (see Fig. I(c» will be measured by a
doorstopper glued on the end of the borehole.
If the configuration of the gauges in the rosette is as shown in Fig. I(e), and they
are glued on the end of the borehole so that the A and B directions are parallel to
the X and Y directions respectively, then the normal stresses cr'A = cr'x and cr'B =
cr'y and "'AB = ,,'XY are given by (see Appendix)
cr'A =cr'x
,
~
-
,
{e1 ~:B
E
crB =cry
=
2
eA
{
+
+ eB
(4)
e1 ~:B}
eA - eB
}
I+v
I-v
. . ... . . .
. . ( 5)
(6)
"'AB = ,,'XY =~ (2eC~~\+eB)}
where E and v are the Young's modulus and Poisson's ratio of the rock and eA, eB
and ec are the strains measured in the A, Band C directions respectively.
If,,' Xy = 0, then cr'x and cr'y are the principal stresses and the directions of the
gauges A and B are parallel with the principal directions.
If,,' Xy #- 0, then cr'x and cr'y are not the principal stresses which are then given by
cr'I,2 =;-
{(l
-
v) (eA
+ eB)
and their directions by
2(eI,2-eA)
tancp' I, 2 =
2ec -
(eA
:::!:::
(l
+ eB)
+ v)
.J{2ec
-
(eA
+ eB)}2 + (eA
-
eB)2}
. .(7)
(8)
where f is measured anti-clockwise from the OA direction as shown in Fig. 1(e).
The stresses in the surrounding rock crx,cryand "XY are then given by substitution
in equations (1), (2) and (3).
(b) Measurements in three boreholes
As will be seen from equations (4), (5) and (6) the normal components of stress
cr'A and cr'B and shear stress component,,' AB on the end of any borehole are easily
obtained from the doorstopper strain readings eA, eB and ec.
If measurements are made in three boreholes inclined at any angle to one another,
it is necessary to resolve the components cr'A,cr'Band "'AB measured in each borehole
in three arbitrarily chosen orthogonal directions in order to bring them into relationship with each other.
310
The 'doorstopper' and triaxial rock stress measuring instruments developed by the C.S.T.R.-E.
February,
R. Leeman
1969
The stress at any point in a body can be defined by six independent stress components ax, ay, az, "t'Xy, "t'yZ and "t'zx with respect to any arbitrarily chosen coordinate system represented by three axes OX, OY and OZ as shown in Fig. 2.
y
Q
---I- 1-1
Q
0
y
(l,m,n)
Fig. 2-Generalised
co-ordinate
system
The normal component of stress a acting on any plane PQR has the direction
cosines I, m and n and is given by
a
by
=
12ax
+ m2 ay + n2 az + 21m"Xy + 2mn
"YZ
+ 2nl"zx
. . . . . . . . . . . . . . . .(9)
The tangential component of stress "T acting in the fT,mE,nTdirection will be given
"T = liT ax + mnT ay + nnT az + (mnT + mEn) "YZ + (niT + nT/) "zx
+(lmT+ITm)"XY
(10)
A similar expression will be given for "TTacting on the ITT,mTT,nTTdirection.
Thus if measurements are made in three orthogonal boreho/es drilled in the OX,
0 Y and OZ directions as shown in Fig. 3, the direction cosines of a'A(t), a'B(t) and
,,'AB(t) in each borehole are given in the table in Fig. 3 and when substituted in
equations (9) and (10) give the components of a'A(t), a'B(t) and ,,'AB(t) namely a'x(t),
a' y(t) and ,,'XY(i), ,,' yz(t) and ,,'ZX(i) in the OX, 0 Y and OZ directionf-.
February, 1969
311
The 'doorstopper'
and triaxial
instruments
developed
by the C.S.f.R.-E.
R. Leeman
0
~
(Dz
BOREHOLE
No.
MEASURED
STRESS
1
2
3
COSI NES
SUBSTITUTING
THE
DIRECTION COSINES
IN EQUATIONS
(14) AND (15)
I
m
n
0lAI1I
1
0
0
0'A11I
0lBI1I
0
1
0
(1IBIII
1:\BI1I
1,0
0,1
0,0
a' AI2J
0
0
1
1
1
0'B121
0
-
=
O\I1)
=
0\111
1:'AB 111= 1:'x YIII
a'A121
=
O'Z 121
-
0'B121 = (1'YI2)
I'f
.fi
1:IABI2J
0,0
0.1.
12
0.1.
12
1:IABI21= 1:~!2)
al AIJ}
1
1..
12
1
1,.fi
0
0
1..
12
1
o,ft.
a'AIJI
=
(1'BIJ)
=
O'Z!J!
.'ABIJI
=
1:' zx IJI
O'BIJI
.1 ABIJ)
Fig. 3-Normal
DIRECTION
0
0,0
(11XIJI
stress components in three boreholes drilled in the OX. OY and OZ directions
The components crx. cry, crZ, 't'Xy, 't'yZ, 't'zx in the surrounding
by substitution in equations (1), (2) and (3) as follows:
cr'A(l)
cr'A(a)
cr'B(l)
cr'B(2)
cr'A(2)
cr'A(a)
and't'AB(l)
=cr'X(I)
=cr'x(a)
=cr'Y(I)
=cr'Y(2)
=cr'Z(2)
=cr'z(a)
='t"XY(l)
=acrx+bcrz
=acrx+bcry
=acry+bcrz
=acry+bcrx
=acrz+bcrx
=acrz+bcry
=a't'XY
't'AB(2) ='t"YZ(2)
=a't'yZ
't'AB(a) ='t"zx(a)
=a't'zx
rock will be found
(11)*
(12)*
(13)*
(14)*
(15)*
(16)*
(17)
(18)
(19)
*Only three of these six equations are required to obtain ox. cry and crz. e.g. cr'X(l). cr'Y(l) and
a'Z(2)' If, however. all six are measured, a useful check on the results is obtained.
------
312
February, 1969
The 'doorstopper'and triaxialrock stressmeasuringinstrumentsdevelopedby the C.S.I.R.-E. R. Leeman
If measurements are made in three coplanar boreholes (a configuration usually
more suited to underground circumstances) a similar procedure to the above is
followed.
Thus, if, as shown in Fig. 4 the three boreholes 1, 2 and 3 are drilled parallel to
and at angles of 82 and 83 respectively to the OZ axis, the direction cosines of each
stress component and their components in the three directions are as shown in the
table in Fig. 4.
y
x
0
, ABIII
(1AIII
Q)
DIRECTION
STRESS
COMPONENT
(1
'AlII
a'BIII
n
,
0
0
,
O'AIII = a~II'
0
0
6'BI11= O'BIII
,'..111 = ,'XY III
,0,
0,'
0,0
0000",
0
o;nO",
O'BI2I
0
,
0
,'ABI21
0006,,0
a,'
O'AI3I
,,06,
O'BI3I
0
,
",6,,0
a,'
"AB 13'
SUBSTITUTING
THE
IN EQUATIONS
m
0',,21
,'AB(l1
Fig. 4-Normal
COSINES
I
'
0
a"'2I=
,;n6,,0
COSINES
1151
0"'21""'6,+(1"121
0;n'6,+21:"XI2I,;n6"",6,
O'BI1'- (1'YI2I
olnt),+,',,",
o;nO""O ,'AO.I ='~~2'
,;n6,
0\131 ",'6 ,+ 0'~3I
O'AI3I
0
DIRECTION
AND
I'"
-
O'BI"- 0',,31
,'ABI3,=,'yn",ln
"0
",'
6,
6,+ 2"'X13101n6, 00.6,
6,+ "X~3I 00,6,
stress components in three boreholes drilled in the xz plane at 8,°, 8,° and 8,° to the OZ ordinate
The components crX,cry, crZ,'t"Xy,'t"yZand 't"zx in the surrounding rock will be
found by substitution in equations (1), (2) and (3) as before (see corresponding
equations for three orthogonal boreholes-(ll)
to (19) ).
Similar procedures are followed for boreholes drilled at any angles to one another.
The 'doorstopper'and triaxialrock stressmeasuringinstrumentsdevelopedby the c.S.I.R.-E. R. Leeman
313
The three principal stresses in the rock (cri =) crI>cr2and crsare the three roots of
the well known equation:
cris- cri2(crx + cry + crz) + cri(crxcry+ crycrz + crzcrx 1"ZX2)
(crx
-
cry crz
-
crx 1"YZ2
cry 1"Zx2
-
-
crz 1"Xy2
+
21"XY
1"yZ
This can be written in the forms
cris+Bcri2+Ccri+D=0
1"Xy2 1"Zx)
1"YZ2 -
= 0 .. (20)
(21)
and
Wis + Wi + ~
where
B
cri = Wi -"3
oc = 1/3 (3C - B2)
~ = 2~ (2BS
9BC
-
.(22)
=0
+ 27D)
Equation (22) has real roots Wl> W2 and Ws if
~2
OCS
4+27<0
and have the values
WI
= 2
x
)
I
-
cos
f3
W2=2 x
)-}
cos
( t + 120°)
Ws = 2 x
)-J
cos
(1- + 240°)
(
where
<p
=
cos-l
i
L
)
~
~/2
-
OCS
-27)
r
Thus it is possible to determine WI>W2 and Ws and hence crI'cr2and crs.
The direction cosines 1;,mi, ni of each principal stress cri = crI'cr2,crsare found by
substitution in equation (9) written as
cri =
1;2 crx
+
mi2
cry
+
ni2
crz
+ 2/i mi 1"xy, 2mi ni 1"yZ + 2ndi 1"ZX
The overcoring technique used with doorstoppers
The overcoring technique used is represented diagrammatically in Fig. 5.
A standard BX diamond coring crown is used to drill the borehole (approximately 2i in. diameter) to the depth in the rock at which it is desired to determine the
stress as shown in Fig. 5(a). The end of the borehole is ground flat and smooth with
specially prepared square faced and flat faced diamond impregnated bits, photographs
of which are shown in Fig. 6.
-----------
314
The 'doorstopper' and triaxial rock stress measuring instruments developed by the c.S.I.R.-E.
:=::::::~::}
IQ)
ex BOREHOlE DRILLED TO THE
REQUIRED
FLATTENED
DIAMOND
DEPTH
AND END
AND POll SHE D WI1H
TOOLS,
:::::::::11
(b)
STRAIN
CELL
BONDED
ON TO END
OF BOREHOlE
AND
STRAIN
READINGS
RECORDED.
~::::g~~
(cl
BOREHOlE
CROWN
EXTENDED
WITH
THEREBY
STRESS
BX OIAMOND
CORING
RELIEVING
THE CORE.
ca::::]
(d)
BX CORE, WITH
STRAIN
CEll
ATTACHED,
REMOVED
AND
STRAIN
READINGS
TAKEN.
Fig. 5- The overcoring technique usiQg a doorstopper
February,
R. Leeman
1969
Fig. 6-The
diamond bits used for drilling tbe BX borehole and preparing
315
tbe end of tbe borehole
The direction in which the borehole is drilled should be parallel to one of the
minor principal stresses as indicated in a previous paragraph if measurements in only
one borehole are to be made. If measurements are being made in three boreholes
to determine the complete state of stress then the directions in which the boreholes
are drilled is governed by the considerations outlined in the previous paragraph.
Having cleaned and dried the end of the borehole, a doorstopper is glued on to it
and strain gauge readings taken when the glue has hardened. The installing tool is
then removed leaving the doorstopper stuck on the end of the hole as shown in
Fig. 5(b).
Using the same EX coring crown as was used to drill the borehole, the length of
the borehole is extended as shown in Fig. 5(c)-thereby relieving the stresses on the
end of the borehole. The core is broken off the end of the hole as shown in Fig. 5(d)
with the doorstopper still attached to it and the strain relieved readings taken from
the doorstopper strain gauges.
The stresses present on the end of the borehole before overcoring may then be
calculated from the change in strain readings as indicated in the previous paragraph.
Description of the doorstopper strain cell equipment
As will be seen from the diagrammatic sketch of one of the strain cells ('doorstopper') in Fig. 7, a rectangular strain gauge rosette (consisting of three strain gauges
316
The 'doorstopper'and triaxialrock stressmeasuringinstrumentsdevelopedby the CS.f.R.-E.
February, 1969
R. Leeman
measuring in the 0 degree (horizontal) 45 degree and 90 degree (vertical) directions) is
moulded into a rubber casting which fills a plastic shell, Four gold plated connector
pins are moulded in the plastic shell, as shown in Fig. 7, in such a way that when they
are plugged into the inserting tool (described later) they effect electrical contact
between the strain gauges and the strain indicating instrument. The connections to
the pins are shown in the lower illustration in Fig. 7.
The presence of a keyway in the plug section of the plastic shell, ensures that the
'doorstopper' can be plugged into the installing tool with only one possible orientation.
4 CONNECTOR PINS
PLASTIC
MOULDED
RUBBER
CASTING
ROSETTE
GAUGE
BODY
1'2"
,.
KEYWAY
VERTICAL
ALIGNED
GAUGE
PIN CONNECTED
GAUGE
WITH
TO 45.
PIN CON NECTED TO
O'
HORIZONTAL
GAUGE
~.
~
COMMON
PIN
PIN CONNECTED
TO 90.
VERTICAL
GAUGE
c
VIEW OF ROSETTE
IN DIRECTION'
x'
LOOKING
THIS CORRESPONDS
TO THE
VIEW LOOKING
DOWN
THE
BOREHOLE
AXIS FROM ITS
MOUTH
Fig. 7-Details
of a doorstopper
317
The diameter of the 'doorstopper' was chosen so that it can be used in a standard
BX diamond drilled borehole which is approximately 2i in. in diameter.
When a 'doorstopper' is installed on the end of a BX borehole, changes in strain
on the surface of the rock resulting from the overcoring operation are transmitted
to the strain indicating instrument via the strain gauges which are glued on the rock.
The rubber and plastic shell serve to protect the strain gauges from damage and
from water during the overcoring operation. Normally, sufficient glue would be used
to ensure that the base of the plastic shell is also glued to the rock surface.
A photograph of doorstoppers is given in Fig. 8, one showing the strain gauge
rosette, the other glued to a short length of core.
Fig. 8-A doorstopper (left) showing the rosette strain gauge and {right} glued to a short length of core
A cross sectional drawing of the installing tool used to glue a doorstopper on
the end of the borehole is given in Fig. 9 and a photograph in Fig. 10. As will be seen
in Fig. 9, the 'doorstopper' and compensating gauge plug into a piston unit which
slides against a compression spring inside a simple brass tubular unit. An orienting
mercury switch is also housed in the piston unit to enable the doorstopper to be
accurately oriented. The electric lead cable is connected to the instrument through
an eight-channel plug. Ventilation holes, visible also in the photograph in Fig. 10,
are machined in the tubular body of the tool to ensure that the temperature of the
disc of rock on which the dummy gauge is glued reaches the same temperature as
that upon which the measuring 'doorstopper' is attached as quickly as possible.
318
'/2' DISC OF
ROCKCORE
ORIENTING
SWITCH
~
\
~
STRAIN CELL\
PLUGGED INTO
TOOL
\
\
SPRING PRESSURE
SWITCH
CONNECTING
PLUG
\
COMPRESSION
SPRING
VENTILATION
doorstopper
ELECTRICAL
CABLE
HOLES
Fig. 9-Doorstopper
Fig. to-The
LEAD
installing
strain cell installing
tool
tool showing a doorstopper
----------
in the foregronnd
February, 1969
R. Leeman
The 'doorstopper'and triaxial rock stressmeasuringinstrumentsdevelopedby the c.S.f.R.-E.
319
R. Leeman
The compensating dummy gauge consists of a 'doorstopper' glued to a 1- in.
length of BX core of the rock in which the stresses are to be measured. In fact, this is
prepared initially by gluing a 'doorstopper' upon the end of the borehole in which the
stresses are to be measured, overcoring and cutting off a 1-in. length from the core
at the end on which the 'doorstopper' is glued. This 'doorstopper' is very easily
plugged into the inner plug of the piston unit and acts as a temperature compensating
dummy gauge.
When the installing tool with a 'doorstopper' plugged into it is pushed up to
the end of the hole by means of specially designed installing rods, and pushed against
the end of the borehole, the piston unit is forced into the tubular body of the tool
against the compression spring until the spring pressure switch, shown in Fig. 9,
closes. A lamp lights up in the control box to which the installing tool is connected
and indicates that the desired load of approximately 10 Ib is being applied to the
'doorstopper'. This must be maintained until the glue has hardened. The installing
tool can then be removed from the borehole leaving the doorstopper glued to the
end of the borehole.
A photograph of the control box is shown in Fig. 11. This houses the electrical
lead, the installing tool, spare doorstoppers, the strain indicator and control panel.
On the control panel are two lamps, one connected to the mercury orienting switch
and the other to the spring pressure switches in the installing tool. A three-way
switch is provided to enable readings from each of the three strain gauges in the
doorstopper rosette to be made in turn.
Glues and rock drying agents used
Any of the commercially available strain gauge cements may be used to glue
the doorstoppers to the rock. Araldite strain gauge cement has been found very
reliable. Its setting time is, however, rather long. The setting time should on the
other hand not be so short that the doorstopper cannot be installed before the glue
has wholly or partly set.
In coal, Philips strain gauge cement No. P.R. 9244/04, a quick &etting cement,
has been successfully used.
The use of a water dispellant has also been proved very beneficial in producing
reliable and consistent gluing on of the doorstoppers. In this connection a 10 per cent
mixture in pure alcohol of Union Carbide Silane Coupling Agent No. A 1120 has
has been found to be very effective15. This enables doorstoppers, and triaxial cells
for that matter to be used in wet rock.
The doorstopper borehole assimulator
The determination of the stresses from the doorstopper strain measurements
described in a previous paragraph require& a knowledge of the elastic moduli of the
rock. Due to the variations in these properties, depending upon the locality and the
reliability of the laboratory methods used to determine them, serious errors can be
introduced in the calculated stress results.
In order to overcome this difficulty a so-called 'borehole assimulator' was
designed in which the stress relieved core to which the doorstopper is glued, is loaded
in such a way as to restore the stresses which existed in it before the core was overcored. Two radial loads at right angles are applied to the core hydraulically and the
oil pressures required to restore the doorstopper strain readings to their values before
overcoring are a measure of the original stresses on the end of the borehole.
~--
--
-
320
The 'doorslopper' and Iriaxial rock stress measuring instruments developed by the c.S.I.R.-E.
Fig. It-The
control box/carrying
case for the doorstopper
equipment
February, 1969
R. Leeman
February, 1969
The 'doorstopper'
and triaxiol
instruments
developed by the C.S.J.R.-E.
321
R. Leeman
It can be shown16, 17that if a cylindrical core is loaded biaxially under the pressures p and q, each uniformly distributed over a quarter of its circumference as
shown in Fig. 12 the radial, tangential and shear stresses at the centre are given by
=!
(Jr
(J{) -!
[(p
+ q) + ~ (p -
q) cos 2eJ
[(p
+ q) -
q) cos 2eJ
~
(p
-
"r{) =.37T(p - q) sin 2e
p
q
q
p
Pig. 12-A
cylindrical
core subjected
to bydraulic
pressures p and q over four equal segments
..----------
322
The 'doorstopper'and triaxialrock stressmeasuringinstrumentsdevelopedby the CS.f.R.-E.
February, 1969
R. Leeman
The radial strains for e = 0°, 45° and 90° are given by Hooke's Law for plane
stress as follows:
eroO = !E[(1
v) (p
-
er45°=
I-v
--ur (p + q)
erooO=
2k [(1
v) (p
-
+ q) + ~ (1 +
v) (p - q)]
+ q) - ~(1 + v) (p
q)]
-
The components of stress on the end of a borehole in a uniform stress field with
principal stresses P and Q are given by
a'r = 1,;5[(p+Q)+(P-Q)COs2e]
a's
T'
=
re =
1';5
+
[(P
1 ~25(P
Q)
-
(P
2e
Q)] cos
-
Q) sin 2e
-
where the value of 1.25 is the factor a referred to in paragraph on page 308.
The radial strains for e = 0°, 45° and 90° are given by Hooke's Law for plane
stress as follows:
eroO = l~i5 [(1 - v) (P + Q) + (1 + v) (P - Q)]
e '°r45 =
e'ruoO=
1,25
2E
(P
l~i5 [(1
+
-
Q)
v) (P
+
Q)
-
(1 + v) (P
-
Q)]
Thus for the state of stress in the core in the assimulator to be identical to that
at the end of the borehole:
eroO = e'roo
e r45 ° =
e' r45°
ergo = e'uoo
Solving for P and Q in terms of p and q we obtain
P = 2,150[(1+~)p +(1 -~)p
Q = 2,150[(1-~)p
(23)
]
+(1 +~) q ]
,
,..(24)
February, 1969
Journal of the South African Institute
The 'doorstopper'
and triaxial
323
of Mining and Metallurgy
instruments
developed
by the C.S.f.R.-E.
R. Leeman
Thus by applying the hydraulic pressures p and q on the rock core to restore the
strain, the original principal stresses P and Q in the rock can be obtained, without
requiring any knowledge of the properties of the rock.
A diagrammatic sketch of an assimulator* is given in Fig. 13 and a photograph
in Fig. 14. As can be seen in Fig. 13, the pressures p and q are applied around the
circumference of the rock core via the neoprene seals which fit snugly around it.
In Fig. 14 the assimulator is shown assembled in a carrying case. Pressure pump
handles, pressure gauges and protractor for orienting the core can be clearly seen in
the photograph.
The assimulator is used as follows: Having obtained the three strain readings
after overcoring, the directions of the principal stresses represented by 6 are determined from equation (8).
The core with the doorstopper glued to it is inserted in the assimulator and
oriented at angle 6. The hydraulic pressures p and q to be applied to the core will
then act in the same directions, relative to the gauges on the core, as the principal
stresses P and Q before overcoring. The pressures p and q required to restore the
strain readings to those before overcoring are obtained and substituted in equations
(23) and (24) to obtain P and Q.
The accuracy of doorstopper stress measurements
Van Heerden15 has carried out tests to determine the accuracy of doorstopper
stress measurements in coal which could by no means be described as the classical
material from the point of view of homogenity, isotropy and continuity assumed in
elastic theory. In these tests large 3 ft X 3 ft X 6 ft high coal specimens were cut
in situ in coal pillars underground and known uniaxial compressive stresses were
applied to them by means of hydraulic jacks. The stresses in the pillars were measured
by means of doorstoppers installed in them and this enabled a comparison to be made
between applied and measured stresses.
The results obtained are included in Table I from which it can be seen that the
vertical stresses a1 obtained by using the assimulator agreed remarkably well with the
applied stresses. The horizontal stresses a2 were zero and very small stresses were
measured.
On the other hand the stresses obtained by calculation using the elastic moduli
determined in compression tests on small cylindrical specimens in an underground
laboratory (to eliminate influences of temperature and humidity changes) in most
instances did not give very good results (see Table I). It must therefore be emphasized
that for materials such as coal reliable results cannot be expected, if they are calculated by multiplying the strain readings by the elastic constants obtained on small
laboratory specimens, and that the assimulator should be used to obtain the stresses
in such materials. It is in fact recommended that the assimulator be used in stress
measurements even in hard homogeneous rock in spite of the fact that reliable results
using the elastic constants can be expected in such rock.
In solid homogeneous rock, consistent and reliable results are easily attainable.
Attention, in this connection is drawn to a recent publication18 in which the results
obtained with doorstoppers were compared with those obtained with a borehole
deformation gauge. The test showed remarkable agreement in the results and demonstrated that the doorstopper was very much easier to use.
*For reasons of accuracy two versions of the assimulator have been developed, one for low
strength rock such as coal, and one for high strength rock such as quartzite,
----
---
324
I
~I
»~....
01
-0I~
- 15'..0
",j:lSd
::1.~<>0 0..ti'5~=E.CI:>';~
<><;;;0."60-
february,
R. Leeman
I
0or)
0or)
M
M
8M
or)
M
°
8M
8M
M
M
M
0\
N
'-0
0\
'<t
M
M
N
M
0\
N
0\
N
0I.~ u '-'
I
bI).'!J
j:Ij:I
~.- 01
","'.
<>::1'"§ ';"'~
0. <> j:I
'-0
..
b
.-u
"'.'"
'"~8U .-j:I<>O;;""..0
ci5.;.~
~<;;;C
~.:0<;;;
15'
o~
'"I
00
r--
or)
00
00
I rr
-
M
00
00
\C
N
r--
N
'"
115
>< ><
=
Q
Z
« 0=:
0=: «=
f-< 1
«
1 :I:
'"
;;>
f-<
0or)
N
~
~
:! z
115
~
« Q
:I:
"' :(Z"'
f-<
f-<
~
~
" Cl:>
Cl:>
......
~
...:I
~
<
f-;
;;> f-<
1
~
~
f;;
U Z
Z
~
0U
U
~
Z ~
:( «
f-< 1
0= Z
"'
Cl:>0
f-< Po.
1 ;;>
~Q
=:
"' Cl:>
"'
~~
Z
~~
=:
~
';"'~
.s<1Ad
uj:I<>O;;"'.-
.- ~<;;;C
""..0
00
or)
M
15'
....
0
~:3
e
....
.;;;
01
'"
.;
<>
e~o;;.;;;~::9
~0.'-' 0
0\
-5
-5
.~
'"8
I
.:0
0
.'!J
:3
<>
~'"
"'<>
gf-5....
.- j:I 0
-g.-3
8
0
<?
......
N
'-0
0\
N
r-'-0
N
r-M
M
~0
0\
N
N
......
M
0
'<t
r--
or)
~0
""!.
......
00
M
M
0
r-N
0
'"
'<t
00
<?
......
\C
0\
N
r--
'<t
'<t
'<t
r--
r-0
I
I
or)
or)
N
N
0
00
M
......
N
'<t
M
'"
'"
0or)
0or)
0or)
0
0\
N
0or)
0or)
0or)
or)
0
or)
M
or)
or)
N
N
0
or)
'"
'"
0
or)
or)
......
°
'<t
or)
or)
N
0\
or)
or)
~J "I
~.!:i.:o 01
[110
or)
00
'<t
0
J
1
~
::E 8
1
or)
8
N
M
'<t
'<t
°N 8M ;:!;
°
8N
'<t
N
\C
'<t
0
00
M
or)
or)
r-M
r-or)
0
0
0
N
......
......
N
'"
'<t
°
+ + + + + + + + + '"+
0
~"'::I
or)
N
~0
N
~I
bI)
.S.2 i>'2
8:.;
8 or)
°
N
i
000
N
M
N
I
I
I
00
0
r-or)
0
r-or)
or)
'-0
0
'-0
r--
I "I
I
I
I
I
0
\C
N
or)
0\
N
......
~0
00
M
0
00
0
§
~or)
M
:;
or)
0
M
M
0
or)
0
0
or)
0\
I
I
"I
"I
or)
'<t
O.
or)
N
'-0
0
M
or)
0
or)
0\
i
or) 0
or) \C
0
or)
° N°
I "I
0 «
u u
~8
or)
0\
'<t
N
'<t
N
I~
j:l8.§
.;.;
",....0""
~....<>-<;;;
'<t
N
M
"""
~.S
I
.;
or)
°
0
.8a'J~
!=:
«
'-0
......
b
or)
M
or)
-
I
I
N
I
N
'<t
0or)
""!.
I "I
~0
I "I
I
0
8
N
I '"I
°
M
N
0
J + '"+ + + + + + + + +
O>~o
....00....
bI) 0 u
<> ~j:I
"'.- 8
<>.-....
~~0'-'
'"
0
or)
or)
00
000 r-or)
~. N
N.
- '-0 '"--
'<t
J
I
or)
r-or)
'-0
'<t
0\
°
r--
8
""!.
......
+ + + + + + + + + +
.
.-.----..----
1969
The 'doorstopper'and triaxialrock stressmeasuringinstrumentsdevelopedby the c.S.f.R.-E. R. Leeman
:Cl..
UJ
Ir
::)
(/I
If)
UJ
Ir
0..
UJ
0::
0
U
:.:
u
0
0::
<
<
I
Z
0
;:::
U
"UJ
(/I
(/I
...J
<
UJ
(/I
UJ
Z
W
0::
0..
.0
UJ
Z
UJ
0::
0
U
:.:
u
0
0::
0
UJ
::)
...J
C>UJ
'0::
0::0
UJU
0..
~
01
.§
;
.«
~t
"
]
~
..!!
ID
ID
0..:.:
8u
(/10
Irlr
0
00
01--
:C"
ID
I
ID
Z
0
I-U
UJ
(/I
~
..
~
325
326
The 'doorstopper'
and triaxial
instruments
developed by the C.S.l.R.-E.
February, 1969
R. Leeman
Fig. 14-An assimulator built into a suitable carrying case
Numerous measurements with doors toppers throughout the world have confirmed
the faith placed in this technique and the doorstopper equipment is now being
commercially manufactured.
THE C.S.I.R.
TRIAXIAL
STRAIN CELL
The c.S.I.R. triaxial strain cell was designed to obtain the complete state of
stress in rock in a single borehole.
The theoretical basis for the measuring technique
The stress at a point in a body is presented by six components, namely three
normal stress components crx, cry, crz and three shear stress components, namely
't'Xy, 't'yZ and 't'zx, as illustrated in Fig. l(a) where the point is 'blown up' to a cube
element.
If a circular hole is drilled in an elastic rock mass subjected to a uniformly
distributed state of stress given by the stress components defined by Fig. 15 the
stress in the vicinity of the hole is changed. With reference to a system of cylindrical
co-ordinates r-e-z, as defined by Fig. 15, the stress at any point r-e-z in the vicinity
of the hole with radius a drilled parallel to the Z-axis, is given by six components,
namely three normal stress components 't'r, aG, az and three shear stress components
---
--~---
February, 1969
327
The 'doorstopper'
and triaxial
't"re, 't"ez, 't"zr, as illustrated in
instruments
developed
by the C.S.l.R.-E.
R. Leeman
Fig. 15.The following six expressions yield the relation-
ship between these components and the components crxetc. of the stress in the rock
mass before the hole was drilled.
crr
TxY
i
crx
=
cry
(1 -~) +
(I + 3:: -
i
cro = ~x
cry
4
'I {2(crx
~)
crx
cos
=
't"rO
--
TOZ
-
(-Tzxsine
+
Trz
=
('t"ZX cos
e + 't"yZ sin
crx -
cry
2
cry
~
(
-
a4
r4
3
~
cry
4~)COS 2e
(] + 3 :: )cos 2e a2
+ 4't"xy
2e
a2
)
+ 272
't"yZ
-
+
. . . . . . . . . . .. . . . ... . . . . . . .. ... . . . ... . . . . . . . (25)
r
1
+ 3::
(1
a2
cry)
-
-
crz
-
~
sin 20
~)
(1 +
crx
-
r
. 2e +
Sin
cos e) (1
e) (1
:; sin 2e}
+
TXY
(1
+
't"xy
+ 3~
...
crz
a4
-
(1
3 r4
)sin 2e (26)
...
a2
+ 2'"f2
. .(27)
)cos 2e.
::)
;:)
(29)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (30)
Elr
y
z
Fig. IS-Stress
(28)
system around a hole in the rock mass
328
The 'doorstopper'
and triaxial
instruments
developed by the C.S.f.R.-E.
February, 1969
R. Leeman
If r = a in equations (25) to (30) expressions for the stresses at any point on the
wall of the borehole are obtained. It will be noticed that at r = a, crr = 0, "rQ = 0 and
"rz = O. This leaves crQ,crz and "Qz which can be measured with a rosette of three
gauges having the same configuration as that used in the doorstoppers.
Thus if the A and B gauges (see Appendix) are lined up with the 6 and Z directions,
i.e. with the circumferential and axial directions of the borehole, crA= crQ,crB= crz
and "AB = "Qz.
In the triaxial strain cell three rosettes are glued to the walls of a borehole as
shown in Fig, 16. Rosette I is glued on at 6 = 1T (on the 'sidewall' of the borehole,
1T
~
(at an
(on the 'roof' of the borehole) and rosette 3 at 6 =
rosette 2 at 6 =
"2
4"
intermediate point between rosettes I and 2). The gauges in each rosette are aligned
as indicated above.
IROSETTE
11
I ROSETTE 21
e =lr/2
e=""
y
z
1ROSETTE
AT
rJ,;-V{2IrJ"rJV)CO528+4,xv
sin2e}+6,
rJo;IOxtC1v)-2(Ox-Ov)oos28-nxv
sin
SIX STRESS
;
dA(;1
28
6x,
<:1v, <:1, ,
+
'YZ,,"x
<:1aI2l}
O,=6AI1I+f{Oao,-crali}
.~
00111=-6x
*OBI2I=36x - ()v
*dal31 :IOx+6v)"'xy
+ 30v
.
'ABI2I--2"x
-2tyz
'Aa",=
ARE
OF
dA",
FOUNO
FROM THE
EQUATIONS
'A8I"=
MARKED
=
"xv+O,
v'21,y,+1:zx)
AS FOLLOWS
*
'Xy;
dX=Y8{3<:1BI2I+6a,,}
Oy = '/8{30a",
'xv,
e
ROSETTE 3
ON AN INTERMEDIATE
POINT
8;7%
2
ON THE ROOF
THE BOREHOLE
OAI,,'2VIOx-0~+O,
.
'Aalil
ROSETTE
OF
OAI";-2VIOx-Ov)+d,
.
;Oalil
:
COMPONENTS
1
ROSETTE'
TIlE SIOEWALL
0" THE BOREHOLE
;
8
TT
, , a
'O,=2'tyz,os8-21:,xsine
THE
3
,yz
,'x'
- 'I. {crBI1Itcr"",-2<:1BO}
;
-
'12'ABIII
- 'I"ABI2'
Fig, 16-The components of stress around the periphery of a borehole measured in the three rosettes
of the triaxial strain cell
The 'doorstopper'and triaxialrock stressmeasuringinstrumentsdevelopedby the CS.f.R.-E. R. Leeman
329
The components of stress at the three measuring points i = 1, 2, 3 (for e = 7T,
~, 7;) (1{)(i) = (1A(i), O"Z(i)= O"B(i)and 1'{)Z(i) = 1'AB(i) are given in Fig. 16. The values
of O"A(i),O"B(i)and 1'AB(i) are obtained
Appendix) from
O"A(i)
=
O"B(i) -
1'AB(i)
=
E
2
eAt
{
l
E
2
+ eBi +
eAt -
+ eBi
eAt -
I-v
E feAt
2
1
-
v
-
2eci - (eAi
{
from the strain gauge readings
1
}
eBi
+v
+ eBi)
1+v
eBi
l+v
}
}
as before (see
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (31)
.. ..
. . .. ...,
..
.. . .
.(32)
..
.(33)
The six stress components in the rock o"x,O"y,O"Z,1'Xy, 1'Zy and 1'zx can then be
obtained from the nine equations in the table in Fig. 16. Obviously, only six equations
are required. Those marked with an asterisk in Fig. 16 have been used for this purpose
and give the expressions for O"x,O"y,1'Xy, 1'xz and 1'Zy in terms of the measured
O"A(i),O"B(i)and 1'AB(i)included at the foot of the table in Fig. 16.
It is in fact unnecessary to use all nine of the gauges in the three rosettes-only
six are required. However, the three gauges which measure the strains in the direction
of the axis of the borehole (the Z or A direction) should give identical readings since
eB(i) = eZ(i) is constant around the circumference of the borehole. All of the results
can in fact be obtained from the following strain readings
Rosette 3
Rosette 1
Rosette 2
or
eA(a)
Direction Z
eA(1)
or
eA(2)
eB(a)
eB(l)
eB(2)
Direction e
ec(l)
ec(2)
Direction 45°
Having obtained O"x,O"y,O"z,1'Xy, 1'yZ and 1'zx the principal stresses and their
directions in the rock can be calculated as indicated on page 311. A computer
programme has however been compiled which enables this information to be obtained
directly from the strain readings.
The technique used for in situ stress measurements
To apply the above results to determine the absolute stress in rock an overcoring
technique is used. A standard NXCU (NX casing) borehole (3-!-in. diameter) is
drilled to the depth at which it is desired to determine the stress-as shown in Fig. 17.
The end of this borehole is ground flat with a suitable diamond flattening bit to ensure
accurate collaring of the EX (1-!-in. diameter) borehole which is drilled into the end
of and concentric with the NXCU borehole for a distance of 18 in. as shown in Fig.
17(b). The flat end surface of the NXCU borehole also ensures the proper plugging
of the EX borehole against ingress of cooling water during the overcoring operation
performed later. The strain cell containing the three strain gauge rosettes is then
inserted into the EX portion of the borehole and the rosettes glued in position midway
along its length as shown in Fig. l7(c). The strain gauge readings are taken when the
glue used to glue the rosettes in position has hardened. The installing tool is removed
330
The 'doorstopper'
and triaxial
instruments
developed by the C.S.I.R.-E.
February, 1969
R. Leeman
from the borehole, leaving the strain cell in the EX portion of the borehole. The
mouth of the EX borehole is plugged to prevent cooling water used during the
following overcoring operation from entering this borehole and damaging the strain
cell. The EX portion of the borehole is next overcored using the NXCU coring crown
used to drill the NXCU portion of the borehole as shown in Fig. 17(d).
-~
-----
la) NXCU
BOREHOLE
WHICH
--
EX
-
DRILLED
- ---
BOREHOLE
THE
-
THE STRESS
---
(b
-
END
TO THE
- - ~-
-
DRILLED
OF
THE
DEPTH AT
IS TO BE DETERMINED
FOR
IS ins ISAY)
(cJ
THREE
ROSETTE GAUGES GLUED IN THE
PORTION OF THE BOREHOLE AND
READINGS. TAKEN
( d)
EX
STRAIN
~~-EX PORTION OF THE BOREHOLE OVERCORED
USING Nxcu CORING CROWN
~. -§(e)
INTO
BOREHOLE
-~"$,,:.
-
-------
-
CYLINDRICAL CORE
READINGS TAKEN
Fig. 17-The
REMOVED AND
--+tSTRAIN
overeoring teehniqne with the triaxial
-~--
strain cell
February,
1969
Journal of the South
The 'doorstopper'
and triaxial
African Institute
331
instruments
developed by the c.S.I.R.-E.
R. Leeman
The cylindrical core containing the rosette is removed from the borehole as
shown in Fig. 17(e) and the stress relieved strain readings taken from each gauge.
The difference in the strain gauge readings before and after overcoring are used to
calculate the required values of crg,crz,crgz and hence crx, cry, crz, 't'Xy, 't'yZ, 't'zx and
thereafter the principal stresses and their directions.
Description of the triaxial strain cell equipment
(i) The strain cell and installing tool
A photograph of a triaxial strain cell is shown in Fig. 18. A photograph and a
drawing of a strain cell showing its various components are shown in Figs. 19 and 20
respectively. From these it can be seen that it consists of five distinct units, four of
which all fit on to the main body unit. The strain gauge rosette unit slides over the
main body unit and the projections on each of the three plugs slide in the rosette
plug guides. The temperature compensating gauge unit plugs into the two pins in
the main body unit. The two end covers also fit over the main body unit and form one
composite unit as shown in Fig. 18.
Fig. I8-The
C.S.I.R. triaxial strain cell
..~
.~.__.-
332
The 'doorstopper' and triaxial rock stress measuring instruments developed by the C.S.I.R.-E.
Fig. 19-Photograph
of triaxial strain cell showing its component parts
---------
February, 1969
R. Leeman
ROSETTE
MAIN
BOOV
333
R. Leeman
UNIT
I
PLUG\ES
\
ROCK DISC
(GLUED TO DUMMV
GAUGE WHEN IN USEI
\
COVER UNIl
\
\
'"
\
\
FRONT
,
'\
\\
TEMPERATURE
CDMPENSA"NG
DUMM'( GAUGE \\
UNIl PtUGS INTO BOOV UNIl
\\
,\
\
\
I
I
I
DUMMV
PLUG
Fig. 20-Exploded
view of the trinial
BACK
COVER
UN"
\
ELEC;RICAL
END
PLUG UNIT
STRAIN GAUGE
ROSETTE UNIl CONSISTING
OF THREE PLUGS
GAUGE
PINS
strain ceO
The cell is installed in the borehole by means of an installing tool illustrated in
Figs. 21 and 22. It plugs into the installing tool as shown in Fig. 21. When this is
done the wedge rod seen in Fig. 22 enters the main body of the cell. The wedge rod
is connected to a piston which is actuated by air pressure through flexible tubing
connected to the air pressure pipe connection. Thus when the piston is forced out
under pressure, the wedge rod moves out and forces out the three rosette units into
contact with sidewalls of the borehole. Thus if glue was smeared on the rosettes
beforehand, pressure is supplied for a sufficiently long length of time for the gauges
to be effectively glued to the sidewalls of the borehole.
As will be seen from Fig. 22, a mercury switch is built into the installing tool to
ensure that the cell is correctly oriented in the borehole.
Seeing that the strain cell is installed in an EX pilot hole (1! in. diameter) drilled
into the end of an N XCV borehole (3! in. diameter), it is necessary to fit the installing
tool into a coupling unit as shown in Fig. 23 whose diameter is just slightly smaller
than 3! in. This is, in turn, connected to the installing rods by which the whole
assembly is pushed into the borehole. Note the electrical lead and compressed air
lines connected to the installing tool in Fig. 23.
It should be noted that on completing a stress relieving cycle the strain cell can
be removed from the rock core, dismantled, the used rosette unit removed and
replaced by a new one*. The cell may then be used again. Furthermore, the temperature compensating dummy gauge unit* is easily replaced by another one when the
cell is to be used in different rocks.
"These units will be available commercially.
--------
334
The 'doorstopper' and triaxial rock stress measuring instruments developed by the C.S.f.R.-E.
Fill:. 2t-The
"""'WG
"""""
cell being plugged into the installing
A" on,"",
Fig. 22-Strain
tool
"'"'C""',""'"
cell installing tool
. -~~.~----_..
'WHO"
February, 1969
R. Leeman
February,
1969
The 'doors/opper' and triaxial rock stress measuring nstruments developed by the C.S.f.R.-E.
Fig. 23- The installing
335
R. Leeman
tool fitted in the coupling unit
(ii) The control box and strain indicator
The control box and strain indicator used are similar to that used with the
doorstopper, shown in Fig. 11. The main difference is in the control panel where a
nine-way switch (connected to the nine strain gauges in the three rosettes) replaces
the three-way switch in the doorstopper control panel.
(iii) Auxiliary equipment
A syringe spray is available for spraying the sidewalls of the EX borehole with
cleaning and water repellant liquids before the cell is installed.
An EX borehole plug is available to plug the mouth of the EX borehole after
the installing tool has been removed and just before overcoring. This ensures that drill
cooling water does not enter the EX borehole and thus damage the strain cell during
the overcoring cycle.
The operations involved in using these units are very simple indeed even at the
end of boreholes 50 ft or more long.
.
--------------.
336
February, 1969
Laboratory and field measurements with triaxial strain cell
Tests with the triaxial strain cell in steel cubes in the laboratory have confirmed
the validity of the method6, 19.
Underground tests conducted to date have given very encouraging results7,9
and have confirmed the decision to release it for manufacture on a commercial basis.
This will make generally available equipment for which there have already been
world-wide enquiries.
REFERENCES
1. LEEMAN,E. R. 'Rock stress measurements using the trepanning stress-relieving technique'.
Mine Quarry Eng., Vol. 30, No. 6, June 1964, pp. 250-255.
2. LEEMAN,E. R. 'The measurement of stress in rock,' Parts I-Ill, J. S.Afr. Inst. Min. Metall.,
Vol. 65, September, October, 1964, pp. 45-114, 254-284.
3. LEEMAN,E. R. 'Absolute rock stress measurement using a borehole trepanning stress-relieving
technique.' Proc. Sixth Symp. on Rock Mechanics, Univ. Missouri, October 1964, pp. 407-426.
4. LEEMAN, E. R. 'Remote measurement of rock stress under development in South Africa.'
Eng. Min. J., Vol. 165, No. 9, September 1964, pp. 104-107.
5. HAYES,D. J. 'The in situ determination of the complete state of stress in rock: The principles
of a proposed technique.' Rep. Coun. Scient. Ind. Res. S.Afr., Meg 404, November 1965.
6. LEEMAN,E. R. 'The in situ determination of the complete state of stress in rock: Laboratory
tests to confirm the validity of a proposed technique.' Rep. Coun. Scient. Ind. Res. S.Afr.,
Meg 463, July 1966.
7. LEEMAN,E. R. 'The in situ determination of the complete state of stress in rock: Underground
measurements at 64/40 Service Incline, Western Deep Levels.' Rep. Coun. Scient. Ind. Res.
S. Afr., Meg 512, November 1966.
8. LEEMAN,E. R. and HAYES,D. J. 'A technique for determining the complete state of stress in
rock using a single borehole.' 1st Int. Congr. on Rock Mechanics, Lisbon 1966, Vol. 11, pp.
17-24.
9. VAN HEERDEN,W. L. 'Measurements of rock stresses at Shabanie Mine, Rhodesia, using the
c.S.I.R. Triaxial Strain Cell.' Rep. Coun. Scient. Ind. Res. S.Afr., Meg 663, April 1968.
10. BIENAWSKI,Z. T. 'Deformational behaviour of fractured rock under multi axial compression.'
Rep. Coun. Scient. Ind. Res. S.Afr., Meg 708, September 1968.
11. BONNECHERE,F. 'A comparative study of in situ rock stress measurements.' M.S. Thesis, Univ.
of Minnesota, February 1967.
12. BONNECHERE,F. and FAIRHURST,C. 'Determination
of the regional stress field from "doorstopper" measurements.' J. S.Afr. Inst. Min. Metal/., Vol. 68, No. 12, July 1968, pp. 520-544.
13. VAN HEERDEN,W. L. 'The effect of end of borehole configuration and stress level on stress
measurements using doorstoppers.' Rep. Coun. Scient. Ind. Res. S.Afr., Meg 626, January 1968.
14. GRAY, W. M. and ToEws, N. P. 'Analysis of accuracy in the determination of the ground
stress tensor by means of borehole devices.' Proc. 9th Rock Mech. Sym., Golden Colorado,
April 1967.
15. VAN HEERDEN,W. L. 'Determination of the accuracy of "doorstopper" stress measurements in
coal.' Rep. Coun. Scient. Ind. Res. S.Afr., Meg 693, August 1968.
16. HENDROS,G. 'The evaluation of Poisson's ratio and the modulus of materials of a low tensile
resistance by the Brazilian (indirect tensile) test with particular reference to concrete.' Austr.
J. of Appl. Science, Vol. 10, No. 3, 1959, pp. 243-268.
17. SALAMON,M. D. G. Private communication.
18. VAN HEERDEN,W. L. and GRANT, F. 'A comparison of two methods for measuring stress in
rock.' Into J. Rock Mech. Min. Sci., Vol. 4, No. 4, 1967, pp. 367-382.
19. LEEMAN,E. R. 'The determination of the complete state of stress in rock in a single boreholelaboratory and underground measurements.'
ll/t. J. Rock Mech. Min. Sci., Vol. 5, No. 1,
January, 1968, pp. 31-56.
The 'doorstopper'and triaxialrock stressmeasuringinstrumentsdevelopedby the c.S.l.R.-E. R. Leeman
337
APPENDIX
THE USE OF A (0°,45°, 90°) THREE GAUGE ROSETTE TO
DETERMINE THE STRESS COMPONENTS AT A POINT
Suppose the strains at any point 0 on the surface to which the rosette is glued
are measured by means of a strain gauge rosette containing three strain gauges
GA, GBand Gc oriented relative to two axes X, Yas shown in Fig. A.
By a simple resolution of the strains in Fig. A it can be shown that the relations
between the strains eA, eB and ec measured by the strain gauge GA, GB and Gc and
the state of strain at 0, are given by:
eA = ex COS2CPA
+ ey sin2cpA+ YXy sin cpAcos cpA
.(A.I)
eB = ex COS2cpB + ey sin2cpB+ YXy sin cpBcos cpB . . . . . . . . . . . . . . . . . . . .(A.2)
ec = ex coscpc + ey sin2cpc+ YXy sin CPccos CPc . . . . . . . . . . . . . . . . . . . .(A.3)
where ex and ey are the normal strains in the X and Y directions and YXy the tangential
strain at O.
If now the strain gauges are arranged as shown in Fig. B such that GA measures
in the direction X, GB in the direction Yand Gc measures at 45° to GA and GB then
CPA
17
= 0,
517
=2
CPB
CPC
="4
and substituting in equations (A. I) eA
(A.3) above we obtain.
= ex
eB = ey
+ ey) + Yxy}
= 1-{(eA + CB) + YAB)}
YAB = 2ec - (eA + eB)
ec = e45°= 1- {(ex
.'.
The magnitudes of the principal strains, e1 and e2 may be calculated from the
strain gauge readings eA, eB and ec given by GA, GB and Gc by substitution in the
following equation:
= 1- {(eA + eB) ::!::~[(eA - eB)2 + YAB2])
. . . . . . . .(AA)
= 1- {(eA + eB) ::!::~(eA - eB)2 + {2ec - (eA + eB)}2])
Their directions may be calculated from the following expressions:
eb 2
-1. t an 2'l-'P
Writing
.
'"(AB
eB -
-
eA
~ [(eA -
SIn 2cpp
=
cos 2cpp
=
eAB
~X
eA
eB)2
=
-
~X
+ eB)
2ec - (eA
eA - eB
+
2ec -
{2ec - (eA
(eA
~X
+ eB)
+ eB) }2] = ~ X
.
(A.5)
eB
.(A.6)
338
v (Z)
x(a)
Fig. A
V(Z)
.8= I
2
fS}'
-E;J-+A=
0 X(a)
.C=ll.
"
Fig.B
~-
---
February,
R. Leeman
1969
February, 1969
The 'doorstopper' and triaxial rock stress measuring instruments developed by the C.S.f.R.-E.
339
R. Leeman
2(el, 2 - eA)
t an '1'1,2=
-I.
2ec - (eA + eB)
Notice, from (AA) that
e1+e2
ande1-e2
-
eA+eB
(A.7)
-
.JX
(A.8 )
Now if 0'1and 0'2are the principal
E
0'1
= I
-
0'2
= I
-
v2
E
V2
(e1
+ ve2)
(e2
+ vel)
stresses on the surface of the borehole.
,
.(A.9)
(A.10)
where E = Young's modulus of the rock
v
= Poisson's ratio of the rock
The components
of the normal stresses O'Aand O'Bin the A and B directions
respectively and the tangential stress "AB are given by:
O'A
O'B
=
=
1-(0'1 +0'2)
(A.ll)
+!(0'1-0'2)cos2cpp
(A.12)
!(0'1+0'2)-!(0'1-0'2)cos2cpp
= HO'l - 0'2) sin 2cpp
In terms of strain, substituting for
..(A.13)
"AB
(A.I3)
O'A
= ~[e1I~e~
O'B
= ~
2
[
= - [E
"AB
2
e1
+
e2
I-v
+
e;~:2
and
0'2
from (A.9) and (A.10) in (A.ll) to
COS2cpp]
e1 - e2
-
0'1
I+v
cos 2cpp
]
e1 - e2.
-I.
I + v sIn 2'1'p
(A.I4)
]
.. .. .'
(A.15)
..
and substituting (A.5) to (A.6) in (A.I4) to (A.I6) we obtain
[ I-v+ + I+v ]
+
= ~[
]
+
-- 2 [
]
I +
O'A =!!.2
O'B
"AB
2
-
E
eA
eB
eA
eB
I-v
-
eA -
eB
eA -
eB
I+v
2ec - (eA
eB)
v
-----
-------
.(A.I6)

`doorstopper` and triaxial rock stress measuring instruments

Transcription

Similar documents

CHOCHA – COMMUNITY SCHOOL, CHITUNGULU

How Women ROCKED THE VOTE in Little Rock

Appendix F

Song List - Gator James Band

Kopanga Clinic Well Report

Sell Sheet - Rock Sake

Presented by Brenda Music: He Grew the Tree by Barbara Mandrell

SS-081 $13.99 “Tales” 06/10/08

Zambia - Connected Church

social raquet - ALEXANDER PARK TENNIS CLUB